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Canoe Stability
Is a flat bottom canoe more stable than a round bottom one or is the round bottom one more stable?
The answer is: "It depends..."  (sorry about that :-\ )

As with life in general, simple answers just don't apply.

The flat bottom will tend to remain parallel to the surface of the water, and just below it, (unless you are carrying a very large number of helium balloons).  If you are canoeing on calm, flat water, then the flat bottom will make for a much more stable ride.  You can shift your weight to greater extremes and not feel that the canoe will rotate under you and tip you out.
Another way to look at it, is that it is easier to keep your centre of gravity over the flatter boat whereas the rounder hull seems to slip out from under you, leaving your centre of gravity over the edge.
If you are in rougher water, the situation is more complex:
If you are on the side of a wave, the water surface, and thus the flat bottom of the boat, may be tipped at a considerable angle.  If you are sitting perpendicular to the bottom, then you might find it very difficult to keep your centre of gravity over the boat. (Depending on the severity of the wave and the height of your seat)
The round bottom boat will tend to rotate so that the water is higher on one side than the other, but it means that you will find it easier to remain vertical and keep your centre of gravity over the boat.

If the boat takes on water, the water will form a shallow layer across the entire bottom of the flat bottom boat, but it will tend to concentrate and be deeper, down the centre line of the rounder boat.
In flat water, this means you have a greater variety of depths of water to place your feet in, which may not be of much concern to you or your feet.

In rough water, the deeper water around the centre line will tend to pull the centre of the boat down, rotating the boat to keep the bottom down.  This will tend to keep the paddler above the centre line of the canoe and in a reasonably vertical position.

As the flat bottom boat tips with the surface of the wave, the shallow pool will suddenly rush to the lower side, and the weight and momentum of it will increase the tendency to tip.  As the boat goes over the wave and tips the other way, the water will suddenly surge to the other side.
The momentum of the water will act to enhance the extremes of the boat motion which will force you into a position that continually places your centre of gravity beyond the edges of the boat.  This, of course, increases the likelihood that you will get to use the PFD that you so-wisely are wearing.

The water in the round boat will also oscillate around the centre point, but due to the shape of the hull, the oscillations will not be as severe and the boat will have a greater tendency to keep its occupants in stable positions.
In reality you will select a canoe that best suits how you will use it, and it will likely be a compromise shape, between the extremes.  If like me, you like to glide through the backwaters on a calm day and examine the flora and fauna beneath you, you will select a flatter canoe.  If you like more adventure, or perhaps you want more speed, then you will want a different style.

Each shape has its advantages and its disadvantages, there is no single best canoe shape or style.

To see some diagrams representing these ideas, click here.